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ufoace



Joined: 11 Mar 2013
Posts: 46

PostPosted: Thu Jan 16, 2014 7:12 am    Post subject: Reply with quote

i only have some icosahedron stars
http://www.youtube.com/watch?v=_&feature=youtu.be
and some icosahedron mutants:
http://youtu.be/4Fv4pCuJVUk
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Apr 27, 2014 8:23 am    Post subject: GridBall-Varations Reply with quote

Variations of an Algebraic Surface call 'GridBall', where you can change the integer value 'n'.

Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
Code:
Name: PG_GridBallN6
/* Isosurface: PG_GridBallN6 4/2014 Gerd Platl */
F(): 0.0001 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 10*(x*x+y*y+z*z-1)^6
[x]: -1.11 , 1.11
[y]: -1.11 , 1.11
[z]: -1.11 , 1.11
;
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Apr 27, 2014 8:41 am    Post subject: Another variation... Reply with quote

This is - hard to believe - another variation of the Gridball.

Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
Code:
Name: PG_RubberStar1
/* Isosurface: PG_RubberStar1 4/2014 Gerd Platl
a variant of PG_GridBallN6
*/
F(): 1 + 79*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - (x*x+y*y+z*z-1)^6
[x]: -4 , 4
[y]: -4 , 4
[z]: -4 , 4
;
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nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Apr 27, 2014 11:35 pm    Post subject: Reply with quote

Hi,
This is a good starting script to animate your gridball. You can define some variables if you need more calculation speed. The problem with your examples is that "n" is an integer but "t" in MathMod scripts is not a discrete variable.
Quote:
{
"Iso3D": {
"Component": [ "GridBall" ],
"Fxyz": [ "0.0001-((x*x-y*y)*(y*y-z*z)*(z*z-x*x))^2-10*(x*x+y*y+z*z-1)^(23+int(20*sin(t*2*pi)))" ],
"Name": [ "GridBall" ],
"Xmax": [ "1.4" ],
"Xmin": [ "-1.4" ],
"Ymax": [ "1.4" ],
"Ymin": [ "-1.4" ],
"Zmax": [ "1.4" ],
"Zmin": [ "-1.4" ]
}

}

_________________
Cheers,
Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Fri May 16, 2014 9:25 am    Post subject: PG_CagedStar1 = PG_GridBallN6 + PG_RubberStar1 Reply with quote

RubberStar meets GridBall - together in harmonie...

Code:
Name: PG_CagedStar1
/* Isosurface: PG_CagedStar1  5/2014  Gerd Platl
   = PG_GridBallN6 + PG_RubberStar1
*/
F(): (4000 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 44*(x*x+y*y+z*z-16)^6)
   * (1 + 89*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 -    (x*x+y*y+z*z-1)^6 )
[x]: -5 , 5
[y]: -5 , 5
[z]: -5 , 5
;
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Fri May 16, 2014 12:41 pm    Post subject: Witch of Maria Agnesi Reply with quote

Todays Google theme is the 296. birthday of Versiera der Maria Agnesi...

Code:
Name: PG_WitchOfAgnesi
X():tan(u)
Y():cos(u)^2*cos(v)
Z():cos(u)^2*sin(v)
[u]:-1.3,  1.3
[v]:0,  2*pi
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sat May 31, 2014 10:59 am    Post subject: A new world record ? Reply with quote

Hi all
Oliver Labs constructed 2004 a surface of degree 7 (septic) with 99 singularities - that's world record.
The maximum number of singularities are 104.

See http://www.algebraicsurface.net/
and http://imaginary.org/gallery/oliver-labs (and press >) for the comprehensive formula.

Martin Heider has published his new septic with more than 99 singularities.
Take a look at http://www.spektrum.com/artikel/950384&_z=798888
Is that a new world record ???



Code:
Name: MH_Septik2
/* Isosurface: MH_Septik2
 Septik mit 105 ??? Singularitäten, Martin Heider
 http://www.spektrum.com/artikel/950384&_z=798888
*/
F():           (x*0.8358                        -(z-0.5)*0.549)
* (x*cos( 2*pi/7)*0.8358 -y*sin( 2*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 4*pi/7)*0.8358 -y*sin( 4*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 6*pi/7)*0.8358 -y*sin( 6*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 8*pi/7)*0.8358 -y*sin( 8*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos(10*pi/7)*0.8358 -y*sin(10*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos(12*pi/7)*0.8358 -y*sin(12*pi/7)*0.8358 -(z-0.5)*0.549)
- (x^2 +y^2 -4.731)^2
[x]: -4.5 , 4.5
[y]: -4.5 , 4.5
[z]: -4.5 , 8
;
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